So the ftr can establish a CAP or move and fight, but not both correct?
Correct. A fighter may not take any other action on the turn that it establishes CAP.
And landing from a CAP does not impede either of these options^?
Also correct. A fighter may function normally on the turn that it lands from CAP. Of course, if it plans on establishing CAP again on that same turn, it may not do anything else.